Statistical and Computational aspects of Wasserstein Barycenters

Abstract: The notion of average is central to most statistical methods. In this talk we study a generalization of this notion over the non-​Euclidean space of probability measures equipped with a certain Wasserstein distance. This generalization is often called Wasserstein Barycenters and empirical evidence suggests that these barycenters allow to capture interesting notions of averages in graphics, data assimilation and morphometrics. However the statistical (rates of convergence) and computational (efficient algorithms) for these Wasserstein barycenters are largely unexplored. The goal of this talk is to review two recent results: 1. Fast rates of convergence for empirical barycenters in general geodesic spaces, and, 2. Provable guarantees for gradient descent and stochastic gradient descent to compute Wasserstein barycenters. Both results leverage geometric aspects of optimal transport. Based on joint works (arXiv:1908.00828, arXiv:2001.01700) with Chewi, Le Gouic, Maunu, Paris, and Stromme.

optimization and controlstatistics theory

Audience: researchers in the topic

MAD+

Series comments: Description: Research seminar on data science

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